
Re: Leaving 0^0 undefined  A numbertheoretic rationale
Posted:
Sep 12, 2013 9:15 AM


On Thursday, September 12, 2013 3:46:49 AM UTC4, Peter Percival wrote: > Dan Christensen wrote: > > > On Wednesday, September 11, 2013 5:09:52 PM UTC4, Peter Percival wrote: > > >> Dan Christensen wrote: > > >> > > >> > > >> > > >>> > > >> > > >>> Show me a contradiction that arises from 0^0 = 0. > > >> > > >> > > >> > > >> The product of the empty set is 1, hence 0^0 = 1. That contradicts 0^0 > > >> > > >> = 0. Therefore 0^0 doesn't = 0. > > >> > > > > > > More convincing would be obtaining a contraction by assuming only 0^0=0 along with the usual rules of naturalnumber arithmetic, including the Laws of Exponents. THAT would be interesting. > > > > Among the usual rules is 0^0=1. >
I don't think so. In any case, as I have suggested, it can be shown, without making that assumption, that there are only 2 binary functions on the natural numbers that satisfy the Laws of Exponents  one has 0^0=1, the other 0^0=0. They give identical results at every other point.
Dan Download my DC Proof 2.0 software at http//www.dcproof.com

